We prove a semi-Riemannian version of the celebrated Morse Index Theorem for geodesics in semi-Riemannian manifolds; we consider the general case of both endpoints variable on two submanifolds. The key role of the theory is played by the notion of the Maslov index of a semi-Riemannian geodesic, which is a homological invariant and it substitutes the notion of geometric index in Riemannian geome...

The comparison theory for the Riccati equation satisfied by the shape operator of parallel hypersurfaces is generalized to semi–Riemannian manifolds of arbitrary index, using one–sided bounds on the Riemann tensor which in the Riemannian case correspond to one–sided bounds on the sectional curvatures. Starting from 2–dimensional rigidity results and using an inductive technique, a new class of ...

The comparison theory for the Riccati equation satisfied by the shape operator of parallel hypersurfaces is generalized to semi–Riemannian manifolds of arbitrary index, using one–sided bounds on the Riemann tensor which in the Riemannian case correspond to one–sided bounds on the sectional curvatures. Starting from 2–dimensional rigidity results and using an inductive technique, a new class of ...

In this paper, we consider an arithmetic Hodge index theorem for a family of semi-stable curves, generalizing Faltings-Hriljac’s arithmetic Hodge index theorem for an arithmetic surface.

In this article we studied Nielsen coincidence theory for maps between manifolds of same dimension without hypotheses on orientation. We use the definition of semi-index of a class, we review the definition of defective classes and study the appearance of defective root classes. We proof a semi-index product formula type for lifting maps and we presented conditions such that defective coinciden...

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Temporal joins are important but very costly operations. While a temporal join can involve the whole time (and/or key) domain, we consider the more general case where the join is defined by some time-key rectangle from the whole space (i.e., when the user is interested in joining portions of the –usually large– temporal data). In the most restrictive join, objects (within this rectangle) are jo...